# Truncate a Hierarchical Clustering tree in order to get the cophenetic coefficient

I've gone ahead and clustered a dataset using a Euclidian Hierarchical Clustering algorithm:

from scipy import cluster

distance_metric = 'euclidean'


I'm then calculating the Cophenetic Coefficient in order to determine the goodness of fit of the clustering:

from scipy.spatial.distance import pdist

cophenetic_corr_coef


However, this calculates the values using the full hierarchical cluster, rather than a pruned one. When I go ahead and plot it, for example, I can specify a p value to truncate the dendogram:

cluster.hierarchy.dendrogram(linkage_matrix,
leaf_rotation=90,
leaf_font_size=12,
# no more than p levels of the dendogram tree are displayed
truncate_mode='level',
p=12,
)


However, I'm not seeing a way to prune the actual model/linkage matrix, rather than simply the depiction of the dendogram of the linkage matrix. How can I go ahead and prune the hierarchical cluster that has been generated in order to calculate the Cophenetic Coefficient for a truncated Hierarchical Clustering algorithm?